For axiom of choice you need to define a function (choice function) with domain I . If I is finite you can define a function by listing all its values. This already can be done based on the other axioms of set theory, so AC is not needed in this case.

Oh right. I thought there was some problem in choosing what the output of the function was.
Okay then, thanks.
If I is countably infinite, you can also specify the function with a list though, surely?
You need a way of deciding what each f(i)=. But even if I is finite, you still need a way of deciding what each f(i)=.
Need help D:

(I understand that the AC isn't needed in choosing from well-ordered sets, so I thought the issue was just deciding how to pick the f(i))